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arXiv:cond-mat/9810259 · Physical review. B, Condensed matter

Massless phases of Haldane-gap antiferromagnets in a magnetic field

Gábor Fáth, P. B. Littlewood

Published Dec 1, 1998• 15 citations
arXivHTMLPDF

Abstract

The behavior of Haldane-gap antiferromagnets in a strong magnetic field is not universal. While the low-energy physics of the conventional one-dimensional spin-1 Heisenberg model in its magnetized regime is described by one incommensurate soft mode, other systems with somewhat perturbed coupling constants can possess two characteristic soft modes in a certain range of the field strength. Such a two-component Luttinger liquid phase is realized above the massive Haldane-gap phase, and in general above any massive nonmagnetic phase, when the ground state exhibits short-range incommensurate fluctuations already in the absence of the field.

DOI
10.1103/physrevb.58.r14709

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The behavior of Haldane-gap antiferromagnets in a strong magnetic field is not universal. While the low-energy physics of the conventional one-dimensional spin-1 Heisenberg model in its magnetized regime is described by one incommensurate soft mode, other systems with somewhat perturbed coupling constants can possess two characteristic soft modes in a certain range of the field strength. Such a two-component Luttinger liquid phase is realized above the massive Haldane-gap phase, and in general above any massive nonmagnetic phase, when the ground state exhibits short-range incommensurate fluctuations already in the absence of the field.
We study the behavior of Heisenberg, antiferromagnetic, integer-spin chains in the presence of a magnetic field exceeding the attendant spin gap. For temperatures much smaller than the gap, the spin chains exhibit Luttinger liquid behavior. We compute exactly both the corresponding Luttinger parameter and the Fermi velocity as a function of magnetic field. This enables the computation of a number of correlators from which we derive the spin conductance, the expected form of the dynamic structure factor relevant to inelastic neutron-scattering experiments, and NMR relaxation rates. We also comment upon the robustness of the magnetically induced gapless phase both to finite temperature and finite couplings between neighboring chains.
We investigate the zero magnetization and ground state phase diagram of a spin-1/2 chain with competing ferromagnetic nearest-neighbor and antiferromagnetic next-nearest-neighbor exchange couplings in the strongly interacting regime. Using density matrix renormalization group (DMRG) simulations, we discover two successive commensurate-incommensurate transitions of the nonconformal Pokrovsky-Talapov universality class, occurring even at zero magnetic field. We argue that the first transition marks the proliferation of solitonic discommensurations (kink-antikink pairs) in a critical phase with central charge c=2, emerging from a period-4 gapped phase. At the second transition, an incommensurate quadrupolar (or nematic) Luttinger liquid forms out of a gapped phase separation, via the condensation of two-magnon bound pairs. In the strongly interacting limit, the location of the two Pokrovsky-Talapov transitions can be analytically predicted with degenerate perturbation theory. Our results demonstrate that frustration alone is sufficient to drive continuous commensurate-incommensurate transitions of Mott type and stabilize complex objects with incommensurate quasi-long-range order without doping.
A quasi-one-dimensional S=1 antiferromagnet with XXZ-type intrachain couplings and Ising-type interchain couplings is studied. It has been suggested that when the interchain couplings are sufficiently small such a system has no long-range order, even at T=0, because of strong quantum fluctuation caused by the Haldane gap. Treating the problem in a restricted Hilbert space which describes the low-energy behavior of S=1 antiferromagnets rather accurately, we prove two theorems which establish the existence of a unique disordered ground state with a gap.
Critical properties of field-induced magnetic phases are investigated in the one-dimensional S=1 Haldane system with planar anisotropy, using the finite-temperature density-matrix renormalization group method. We point out that the underlying physics of the properties differs significantly between cases of different field directions: The magnetic phase is characterized as the gapless Tomonaga-Luttinger regime in one case and as the gapful soliton regime in the other. In connection with the information obtained for the one-dimensional spin chain, possible implications for the field-induced magnetic long-range ordering are discussed.
The antiferromagnetic Heisenberg spin chain with integer spin has a short-range magnetic order and an excitation energy gap above the ground state. This so-called Haldane gap is proportional to the exchange coupling constant J of the Heisenberg chain. In this study, we discuss recent results about the spin dependence of the Haldane gap and conjecture an analytical formula valid asymptotically for large spin values. We then discuss the robustness of the edge states of the spin-1 chain by studying a spin-1 ladder using the density matrix renormalization group (DMRG) algorithm. We show that the peculiar hidden topological order of the spin-1 chain disappears smoothly by increasing the ladder rung coupling without any intervening phase transition. This is evidence for the fragile character of the topological order of the spin-1 chain.
We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.